One lesser known wee screen appearance for the Big Yin, however, was a starring role in classic US detective crime series Columbo.
5USA viewers were treated to a re-run of the episode on Sunday afternoon, with many taking to social media to note their surprise at seeing Sir Billy appear alongside Peter Falk.
Columbo’s sometime actor/director Patrick McGoohan snapped up Connolly in place of himself for the penultimate episode of the long-running detective drama.
Broadcast in 2000, Episode 68: Murder with Too Many Notes saw Connolly appear as Findlay Crawford, an Oscar-winning composer whose ghostwriter, Gabe, threatens to very publicly lift the lid on the true author of his most successful work.
Fearing his career will be dead and buried if the world ever learns the truth, Connolly’s character drugs his antagonist before cleverly arranging his death without leaving a fingerprint.
Peter Falk’s Los Angeles super sleuth is called in to solve the murder - a murder which Falk later described as “one of the most ingenious” in the history of Columbo.
Connolly’s conniving composer succeeds for much of the 120 minutes (this was a TV movie rather than a standard episode) in deflecting suspicion and evading capture but is inevitably snared in classic Lt Columbo fashion.
One smirk-inducing bit of trivia is Sir Billy’s decision to name his character Findlay Crawford, a knowing nod to an old stand up routine in which the comic tears in to rich parents who give their offspring last names for first names.
But despite Connolly having tasted (then recent) success opposite Dame Judi Dench in the critically-acclaimed Mrs Brown, rumour has it McGoohan was left regretting his decision to enlist the Scottish showman.
According to online movie database IMDb, McGoohan was furious at Connolly for turning up drunk and failing to learn his script.
In one scene involving Columbo and the killer, it is claimed the director yelled cut and accused the Big Yin of slurring his dialogue.
Actor and director then engaged in a heated verbal exchange before Connolly appeared back on set around half an hour later with renewed vigour and an enhanced knowledge of his remaining dialogue.
Findlay Crawford was written in to the show as a hard drinker, so perhaps McGoohan wasn’t too chuffed with Connolly’s attempts at method acting.
Murder with Too Many Notes was widely panned upon its release and remains one of the lowest rated episodes on IMDb from the Columbo canon.
However, in a tribute to Lt Columbo himself, if there is ‘just one more thing’ to mention, it’s never to judge a show too harshly on its internet rating - the scene in which Falk and Connolly duet That’s Amore together is television gold and absolutely worth a gander.